It is known from Patent Specification No. GB-A-688144 (Korber) to make booklets of folded and zig-zag interleaved cigarette papers by withdrawing paper strip from a plurality of supply rolls or bobbins, folding and interleaving the strips by passage through a succession of combs to form a folded and interleaved strand, and cutting the strand to form booklets. But the machine employed by Korber had a stationary cutting knife which was impractical for high speed operation and did not make a clean transverse cut through the strand which is required to move continuously. U.K. Pat. No. 2165080 (Kastner) describes a similar machine in which the knife is mounted on a movable knife plate carried by a platform that is reciprocally movable in a direction parallel to the direction of travel of the strand of interleaved paper strips. A cylinder or other means carried by the platform reciprocally moves the knife plate towards or away from the strand so that the knife follows the movement of the strand as it severs the strip. A pusher plate carried by and movable with the knife plate displaces a severed booklet or packet sideways with respect to the line of travel of the strand. But the Kastner machine still presents a number of disadvantages. Reciprocation of the platform is by an eccentric on a drive wheel that is coupled to the platform by a pivoted link, so that the platform does not match the speed of the strand throughout its rearward stroke, but instead its velocity varies in simple harmonic motion. Since the knife is moved towards and away from the strand without any component of motion across it, cutting is not as efficient as it could be. Cut booklets are discharged sideways into a magazine which is joined to the reciprocating platform by means of a flexible portion, which is essential because movement of the pusher is not separated from that of the knife.